Let M = ∫ 0 2 π sin θ d θ , then

Clearly π 2 θ < sin θ < θ ∀ θ ∈ [ 0 , 2 π ] ⇒ π 2 ∫ 0 2 π θ d θ < m < ∫ 0 2 π θ d θ ⇒ 3 π < m < 3 2 π 2 3

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationProperties Involving Inequalities (Approximation)Easy2 minQB

MathematicsEasymultiple choice

Let $M = \int_{0}^{\frac{π}{2}} sin θ d θ$ , then

Answer:

A, B, C, D

Solution:

Clearly $\frac{2 θ}{π} < sin θ < θ \forall θ \in [0, \frac{π}{2}]$

$\Rightarrow \frac{2}{π} \int_{0}^{\frac{π}{2}} θ d θ < m < \int_{0}^{\frac{π}{2}} θ d θ \Rightarrow \frac{π}{3} < m < \frac{π ^{\frac{3}{2}}}{3 2}$

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Properties Involving Inequalities (Approximation)

⏱ 2mℹ️ Source: QB

Loading discussions...